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46735-G6
Theoretical Investigation of the Two-state Model for the Excess Electron in Saturated Hydrocarbon Liquids Based on Path Integral Simulation

Seogjoo Jang, Queens College of the City University of New York

During the last funding period, the principal investigator (PI) has completed the computational code for the path integral centroid molecular dynamics (CMD) simulation of the excess electron.  This code allows description of the real time quantum dynamics of the electron and provides direct understanding of how the dynamics of the electron is correlated with the local arrangement of surrounding solvent molecules that are also dynamically evolving.   As a test, the computational code has been implemented for the simulation of an excess electron in supercritical helium for which well-established interaction parameters are available.   Figure 1 provides representative samples of the electron (centroid) trajectories.

Figure 1. Three representative trajectories (x-components of the coordinate) of the path integral centroid centroid of the electron.  The unit of length is chosen to be  ulength=15.3 Angstrom.

For each trajectory in Fig. 1, the electron rattles around a localized region during most of its time.  However, once in a while (about 0.5 picosecond), it goes through a significant jumping motion.    It is obvious that the latter motion makes major contribution to the mobility of the electron.   This is reminiscent of the two-state model for the mobility of the excess electron in hydrocarbon liquids, and is quite contrary to the widely accepted notion that the electron in supercritical helium remains localized (in the concentration tested for the simulation) and is dragged along the motion of helium atoms.   Further examination of this issue will be made for more extensive set of simulation, and a paper reporting the results will be submitted during the next funding period.

The above analysis demonstrates the capability of the CMD simulation in revealing short time real time dynamics that are statistically minor but can make significant contribution to the mobility of the electron.   This demonstrates that the CMD simulation can be used as a valuable tool for investigating the two-state model for the mobility of electrons in hydrocarbon liquids.  As the first step for such CMD simulations, a computational program has been developed for the imaginary time path integral simulation of the excess electron in liquid methane, the simplest hydrocarbon liquid in which the electron is delocalized substantially.  This system represents the other extreme where the electron is believed to go through coherent quantum dynamical motion most of its time.   During the next funding period, imaginary time path integral simulations will be first performed for this system in order to get quantitative information on the degree of delocalization of the electron and its correlation with the nature of the arrangement of solvent molecules. 

For the simulation of the excess electron in larger hydrocarbon liquids, more works need to be done for the identification of reliable model potentials.    A collaborator with good expertise in the modeling of potential parameters has been sought for since the beginning of this proposal, and a postdoctoral researcher partly supported by this grant will start working on this subject in November, 2008.  With the development of the model potentials, path integral simulations for larger hydrocarbon liquids will be performed by extending that of methane.

In the course of the research, it has become clear that a new quantum dynamics method that can provide a reliable description of the coherent quantum dynamics of the electron is needed.  The PI has made significant effort to address this issue, and has been developing a new theoretical approach combining quantum master equation (QME) formalism with a polaron transformation.   This approach overcomes the typical weak-system coupling limit of existing QME approaches, and can establish quantitative understanding of the origin and the effects of the quantum coherence on the dynamics of electron.   An application of a simple version of this theory to a related problem, the resonance energy transfer of electronic excitation, has been made in collaboration with other researchers and has been published in the Journal of Chemical Physics as a Communication in September, 2008.  During the next funding period, the new QME formalism will be extended to multi-state systems.  Then, application of the multi-state theory will be made to the dynamics of an electron solvated in samples of hydrocarbon liquids obtained from the snapshots of path integral simulation.  Incorporation of the QME calculation with the path integral simulation will provide reliable description of the dynamics of the electron in both incoherent and coherent regimes, and thus will elucidate whether the two-state model indeed characterizes its major mechanism of motion in hydrocarbon liquids.

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